Algebra 2 Problems of the Day

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June 2017, Part II

All Questions in Part II are worth up tp 2 credits. Partial credit is possible.


31. Write (x)^(1/3) * (x)^(1/2) as a single term with a rational exponent.

Answer:
First of all, please look at the image. This is how the question was asked. I typed it the best way that I could for this medium.
That said, you're first step is to rewrite the equation as:

(x)^(1/3) * (x)^(1/2)
Now use the rules of exponents:
(x)^(1/3) * (x)^(1/2) = (x)^(5/6)

Leave your answer in this form with the rational (fractional) exponent. Do NOT rewrite it with a radical symbol.

Note: (1/3) + (1/2) = (2/6) + (3/6) = (5/6)

32. Data collected about jogging from students with two older siblings in the table below.

	Neither Sibling Jogs	One Sibling Jogs	Both Sibling Jog
Student Does Not Jog	1168	1823	1380
Student Jogs	188	416	400

Using these data, determine whether a student with two older siblings is more likely to jog if one sibling jogs or if both siblings job. Justify your answer.

Answer:
Sum up the second and the third columns. The number of students with one sibling who jogs is 1823 + 416 = 2239. The number of students with two siblings who jog is 1380 + 400 = 1780.

The probability that a student jogs if one sibling jogs is
P(student | one sibling) = 416/2239 = .186

The probability that a student jogs if both siblings jog is
P(student | both sibling) = 400/1780 = .225

It is more likely that a student with two older siblings will jog if both of their older siblings jog.



Comments and questions welcome.

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